8. (15 points) (a) Use the two-point forward difference formula and the two-point backward difference formula to approximate f'(0.2) separately. (b) Use the most accurate three-point formula to find f'(0), ƒ'(0.1), ƒ'(0.2), and f'(0.3). f(x) x 0 0.1 0.2 0.3 0 0.001 0.008 0.027

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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8. (15 points)
(a) Use the two-point forward difference formula and the two-point backward difference formula to
approximate f'(0.2) separately.
(b) Use the most accurate three-point formula to find f'(0), ƒ'(0.1), ƒ'(0.2), and f'(0.3).
f(x)
X
0
0.1
0.2
0.3
0
0.001
0.008
0.027
Transcribed Image Text:8. (15 points) (a) Use the two-point forward difference formula and the two-point backward difference formula to approximate f'(0.2) separately. (b) Use the most accurate three-point formula to find f'(0), ƒ'(0.1), ƒ'(0.2), and f'(0.3). f(x) X 0 0.1 0.2 0.3 0 0.001 0.008 0.027
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